Trigonometry Examples

$\frac{y^{2}}{y - 3} \cdot \frac{y^{2} - y - 6}{y^{2} + y}$

Step 1

Factor $y^{2} - y - 6$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 1.2

Write the factored form using these integers.

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y^{2} + y}$

Step 2

Simplify terms.

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Step 2.1

Factor $y$ out of $y^{2} + y$ .

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Step 2.1.1

Factor $y$ out of $y^{2}$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y \cdot y + y}$

Step 2.1.2

Raise $y$ to the power of $1$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y \cdot y + y^{1}}$

Step 2.1.3

Factor $y$ out of $y^{1}$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y \cdot y + y \cdot 1}$

Step 2.1.4

Factor $y$ out of $y \cdot y + y \cdot 1$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Step 2.2

Cancel the common factor of $y$ .

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Step 2.2.1

Factor $y$ out of $y^{2}$ .

$\frac{y \cdot y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Step 2.2.2

Cancel the common factor.

$\frac{y \cdot y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Step 2.2.3

Rewrite the expression.

$\frac{y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y + 1}$

Step 2.3

Cancel the common factor of $y - 3$ .

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Step 2.3.1

Cancel the common factor.

$\frac{y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y + 1}$

Step 2.3.2

Rewrite the expression.

$y \cdot \frac{y + 2}{y + 1}$

Step 2.4

Combine $y$ and $\frac{y + 2}{y + 1}$ .

$\frac{y (y + 2)}{y + 1}$